DATE: 11/12/2007 TIME: 13:51 L I S R E L 8.80 BY Karl G. J”reskog & Dag S”rbom This program is published exclusively by Scientific Software International, Inc. 7383 N. Lincoln Avenue, Suite 100 Lincolnwood, IL 60712, U.S.A. Phone: (800)247-6113, (847)675-0720, Fax: (847)675-2140 Copyright by Scientific Software International, Inc., 1981-2006 Use of this program is subject to the terms specified in the Universal Copyright Convention. Website: www.ssicentral.com The following lines were read from file E:\Class Files\kjmu.ls8: Kenny-Judd (1984) example -- Marsh unconstrained approach DA NI=9 NO=500 MA=CM LA x1 x2 z1 z2 x1_z1 x1_z2 x2_z1 x2_z2 y CM FI=KJEXAMPL.CM ME 0 0 0 0 0 0 0 0 5.0 SE y x1 x2 z1 z2 x1_z1 x2_z2 / ! selecting the product of the first measures ! and the product of the second measures MO NY=1 NE=1 NX=6 NK=3 PS=SY PH=SY GA=FU,FR C LX=FU,FI LY=FU,FI TD=SY TE=SY,FI KA=FI AL=FR TY=FI LE ETA_Y LK X Z XZ ! Here's the main effects measurement model VA 1.0 LY(1,1) VA 1.0 LX(1,1) LX(3,2) FR LX(2,1) LX(4,2) ! Unconstrained--let PHI be free !FI PH(3,1) PH(3,2) !CO PH(3,3) = PH(1,1) * PH(2,2) + PH(2,1)^2 ! Here is Marsh's specification for Kappa CO KA(3) = PH(2,1) ! Unconstrained--just estimate these loadings (except for reference var) VA 1.0 LX(5,3) ! CO LX(6,3) = LX(2,1) * LX(4,2) FR LX(6,3) ! Unconstrained--estimated error variances freely ! CO TD(5,5) = PH(1,1) * TD(3,3) + PH(2,2) * TD(1,1) + TD(1,1) * TD(3,3) ! CO TD(6,6) = PH(1,1) * TD(4,4) * LX(2,1)^2 + PH(2,2) * TD(2,2) * LX(4,2)^2 C ! + TD(2,2) * TD(4,4) OU AD=OFF RS MI Kenny-Judd (1984) example -- Marsh unconstrained approach Number of Input Variables 9 Number of Y - Variables 1 Number of X - Variables 6 Number of ETA - Variables 1 Number of KSI - Variables 3 Number of Observations 500 Kenny-Judd (1984) example -- Marsh unconstrained approach Covariance Matrix y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 2.17 x1 -0.37 2.40 x2 -0.18 1.25 1.54 z1 0.40 0.45 0.20 2.10 z2 0.28 0.23 0.12 1.14 1.37 x1_z1 2.56 -0.37 -0.07 -0.15 -0.13 5.67 x2_z2 0.97 -0.05 -0.04 0.04 -0.04 1.34 Covariance Matrix x2_z2 -------- x2_z2 1.96 Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- 5.00 - - - - - - - - - - Means x2_z2 -------- - - Kenny-Judd (1984) example -- Marsh unconstrained approach Parameter Specifications LAMBDA-X X Z XZ -------- -------- -------- x1 0 0 0 x2 1 0 0 z1 0 0 0 z2 0 2 0 x1_z1 0 0 0 x2_z2 0 0 3 GAMMA X Z XZ -------- -------- -------- ETA_Y 4 5 6 PHI X Z XZ -------- -------- -------- X 7 Z 8 9 XZ 10 11 12 PSI ETA_Y -------- 13 THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 14 15 16 17 18 19 ALPHA ETA_Y -------- 20 KAPPA X Z XZ -------- -------- -------- 0 0 Constr'd Kenny-Judd (1984) example -- Marsh unconstrained approach Number of Iterations = 19 LISREL Estimates (Maximum Likelihood) LAMBDA-Y ETA_Y -------- y 1.00 LAMBDA-X X Z XZ -------- -------- -------- x1 1.00 - - - - x2 0.53 - - - - (0.11) 5.02 z1 - - 1.00 - - z2 - - 0.72 - - (0.07) 9.67 x1_z1 - - - - 1.00 x2_z2 - - - - 0.37 (0.03) 11.52 GAMMA X Z XZ -------- -------- -------- ETA_Y -0.11 0.34 0.72 (0.04) (0.05) (0.05) -2.88 7.07 13.57 Covariance Matrix of ETA and KSI ETA_Y X Z XZ -------- -------- -------- -------- ETA_Y 2.20 X -0.40 2.30 Z 0.43 0.22 1.55 XZ 2.59 -0.31 -0.10 3.62 Mean Vector of Eta-Variables ETA_Y -------- 5.10 PHI X Z XZ -------- -------- -------- X 2.30 (0.47) 4.93 Z 0.22 1.55 (0.07) (0.19) 3.12 7.99 XZ -0.31 -0.10 3.62 (0.16) (0.14) (0.41) -1.95 -0.74 8.88 PSI ETA_Y -------- 0.16 (0.12) 1.31 Squared Multiple Correlations for Y - Variables y -------- 1.00 THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 0.05 0.87 0.51 0.55 2.10 1.46 (0.44) (0.14) (0.15) (0.08) (0.27) (0.10) 0.11 6.31 3.38 6.49 7.89 14.91 Squared Multiple Correlations for X - Variables x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 0.98 0.43 0.75 0.60 0.63 0.26 ALPHA ETA_Y -------- 4.95 (0.04) 111.29 KAPPA X Z XZ -------- -------- -------- - - - - 0.22 (0.07) 3.12 Goodness of Fit Statistics Degrees of Freedom = 15 Minimum Fit Function Chi-Square = 16.60 (P = 0.34) Normal Theory Weighted Least Squares Chi-Square = 16.89 (P = 0.33) Estimated Non-centrality Parameter (NCP) = 1.89 90 Percent Confidence Interval for NCP = (0.0 ; 16.24) Minimum Fit Function Value = 0.033 Population Discrepancy Function Value (F0) = 0.0038 90 Percent Confidence Interval for F0 = (0.0 ; 0.033) Root Mean Square Error of Approximation (RMSEA) = 0.016 90 Percent Confidence Interval for RMSEA = (0.0 ; 0.047) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.97 Expected Cross-Validation Index (ECVI) = 0.12 90 Percent Confidence Interval for ECVI = (0.098 ; 0.13) ECVI for Saturated Model = 0.11 ECVI for Independence Model = 2.01 Chi-Square for Independence Model with 21 Degrees of Freedom = 988.70 Independence AIC = 1002.70 Model AIC = 58.89 Saturated AIC = 56.00 Independence CAIC = 1039.20 Model CAIC = 168.39 Saturated CAIC = 202.01 Normed Fit Index (NFI) = 0.98 Non-Normed Fit Index (NNFI) = 1.00 Parsimony Normed Fit Index (PNFI) = 0.70 Comparative Fit Index (CFI) = 1.00 Incremental Fit Index (IFI) = 1.00 Relative Fit Index (RFI) = 0.98 Critical N (CN) = 904.74 Root Mean Square Residual (RMR) = 0.061 Standardized RMR = 0.028 Goodness of Fit Index (GFI) = 0.99 Adjusted Goodness of Fit Index (AGFI) = 0.99 Parsimony Goodness of Fit Index (PGFI) = 0.53 Kenny-Judd (1984) example -- Marsh unconstrained approach Fitted Covariance Matrix y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 2.20 x1 -0.40 2.35 x2 -0.22 1.23 1.53 z1 0.43 0.22 0.12 2.06 z2 0.31 0.16 0.08 1.12 1.36 x1_z1 2.59 -0.31 -0.17 -0.10 -0.08 5.72 x2_z2 0.97 -0.12 -0.06 -0.04 -0.03 1.35 Fitted Covariance Matrix x2_z2 -------- x2_z2 1.96 Fitted Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- 5.10 - - - - - - - - 0.22 Fitted Means x2_z2 -------- 0.08 Fitted Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y -0.01 x1 0.04 0.04 x2 0.04 0.02 0.01 z1 -0.02 0.23 0.09 0.04 z2 -0.03 0.07 0.03 0.02 0.01 x1_z1 -0.01 -0.06 0.10 -0.04 -0.06 0.00 x2_z2 0.01 0.07 0.02 0.08 -0.01 0.01 Fitted Residuals x2_z2 -------- x2_z2 0.00 Fitted Residuals for Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- -0.10 - - - - - - - - -0.22 Fitted Residuals for Means x2_z2 -------- -0.08 Standardized Residuals for Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- -2.08 - - - - - - - - -2.04 Standardized Residuals for Means x2_z2 -------- -1.31 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.06 Median Fitted Residual = 0.02 Largest Fitted Residual = 0.23 Stemleaf Plot - 0|66 - 0|43211100 0|111122234444 0|7789 1|0 1| 2|3 Standardized Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y -2.88 x1 2.82 2.88 x2 0.83 2.88 2.88 z1 -0.97 3.23 1.28 2.88 z2 -0.73 1.20 0.57 2.88 2.88 x1_z1 -0.93 -1.38 1.00 -0.75 -0.81 -0.31 x2_z2 0.55 0.92 0.25 1.08 -0.24 0.65 Standardized Residuals x2_z2 -------- x2_z2 0.58 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -2.88 Median Standardized Residual = 0.74 Largest Standardized Residual = 3.23 Stemleaf Plot - 2|9 - 1|40 - 0|987732 0|2666689 1|0123 2|8999999 3|2 Largest Negative Standardized Residuals Residual for y and y -2.88 Largest Positive Standardized Residuals Residual for x1 and y 2.82 Residual for x1 and x1 2.88 Residual for x2 and x1 2.88 Residual for x2 and x2 2.88 Residual for z1 and x1 3.23 Residual for z1 and z1 2.88 Residual for z2 and z1 2.88 Residual for z2 and z2 2.88 Kenny-Judd (1984) example -- Marsh unconstrained approach Qplot of Standardized Residuals 3.5.......................................................................... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . . . . . . x . . . . N . . x . o . . x . r . . * . m . . x . a . . x x . l . . xx . . . x . Q . . xx . u . . * . a . . x . n . . x x . t . . xx . i . x . l . .xx . e . .x . s . . x . . . . . .x . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -3.5.......................................................................... -3.5 3.5 Standardized Residuals Kenny-Judd (1984) example -- Marsh unconstrained approach Modification Indices and Expected Change No Non-Zero Modification Indices for LAMBDA-Y Modification Indices for LAMBDA-X X Z XZ -------- -------- -------- x1 8.29 5.00 0.91 x2 - - 0.28 0.65 z1 6.22 8.29 0.05 z2 0.78 - - 0.20 x1_z1 0.96 0.72 8.29 x2_z2 0.96 0.72 - - Expected Change for LAMBDA-X X Z XZ -------- -------- -------- x1 1.85 0.13 -0.06 x2 - - -0.02 0.03 z1 0.09 1.85 0.01 z2 -0.02 - - -0.01 x1_z1 -0.10 -0.12 -1.85 x2_z2 0.04 0.04 - - No Non-Zero Modification Indices for GAMMA No Non-Zero Modification Indices for PHI No Non-Zero Modification Indices for PSI Modification Indices for THETA-DELTA-EPS y -------- x1 1.24 x2 1.24 z1 0.50 z2 0.50 x1_z1 1.39 x2_z2 1.39 Expected Change for THETA-DELTA-EPS y -------- x1 0.15 x2 -0.08 z1 -0.14 z2 0.10 x1_z1 -1.58 x2_z2 0.59 Modification Indices for THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 - - - - z1 5.11 0.27 - - z2 0.94 0.15 - - - - x1_z1 3.49 2.62 0.05 0.02 - - x2_z2 1.36 0.50 2.25 1.22 - - - - Expected Change for THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 - - - - z1 0.14 -0.02 - - z2 -0.05 0.01 - - - - x1_z1 -0.22 0.12 -0.03 -0.01 - - x2_z2 0.08 -0.04 0.09 -0.05 - - - - No Non-Zero Modification Indices for TAU-Y No Non-Zero Modification Indices for ALPHA Modification Indices for KAPPA X Z XZ -------- -------- -------- 0.03 0.00 4.79 Expected Change for KAPPA X Z XZ -------- -------- -------- -0.01 0.00 -0.23 Maximum Modification Index is 8.29 for Element ( 1, 1) of LAMBDA-X Time used: 0.010 Seconds